Group/Multiplication/Bijective/Homomorphism/Exercise

Let $G$ be a group, and $g\in G$ be a group element. Let

$\phi :G⟶G,h⟼hg,$

be the multiplication with $g$. Show that $\phi$ is bijective, and that $\phi$ is a group homomorphism if and only if $g=e_G$.

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